The distribution of runs per over (RPO) scored in one-day international cricket does not follow a known distribution. Bailey and Clarke (2008) used multiple linear regression to identify and weight 14 highly significant variables found to be independently predictive of RPO. This paper expands on this work by comparing a range of possible distributions for modeling RPO using both standard and novel approaches. Predictive capacity was determined by developing parameter estimates using 75% of the available 55000 overs and applying the subsequent prediction models to the remaining 25% of the data. Goodness of fit was determined by averaging the log of the predicted probabilities for the actual runs scored with the model producing the highest average indicative of the best fit to the data. Of the 10 approaches examined, a slivered binomial approach appeared to produce the best fit to the data, although due to the increased number of models required, considerable care is needed to ensure that the data is not over-fitted. Both the ordinal logistic regression and the negative binomial approach produced good fits to the data and were more simplistic in implementation. Although not significantly different from each other, these three approaches were significantly better than the remaining seven models that were considered (p<0.0001).